Are there any limitations on the size of the cookie? Also, is this browser dependent?
The "official" maximum size is 4KB, but I would prefer to keep it well under that: no more than a few hundred bytes, tops.
The reason is that cookies are transmitted from the client to the server with every single request - even when requesting images, css and js files (if they reside on the same host something you should avoid in general, but for small sites may not be worth the bother). That means that you'll be requiring the client to transmit 4KB for every request - remembering also that most consumer broadband has much slower upload speed than download speed.